A mathematical model of transport processes throughout the mammalian kidney has been developed. Structural features of the model include labyrinth and medullary ray subsystems in the cortex, distinct vasa recta and capillary plexus subsystems in the outer and inner stripes, and an inner zone subsystem. Distinctions are also made between short and long nephrons, juxtamedullary and non-juxtramedullary nephrons, vasulature, and interstitial spaces. Salt, urea, plasma proteins, and miscellaneous "non-reabsorbable" solutes in tubular and interstitial fluids are chosen as the essential solutes for describing renal mass transport. Whereas geometric and number density data of vessels are taken from anatomical studies, membrane parameters are principally derived from isolated tubule perfusion, micropuncture experiments, and to a limited extent ultrastructural studies. Numerical solutions of the resulting large set of mass transport equations are obtained to simulate the anti-diuretic state of a Brattleboro rat. Computer simulations show that with two distinct interstitial subsystems in the inner stripe, the amount of urea excreted from the terminal collecting ducts and recirculated through the loop of Henle is significantly increased. Simulations also predict that the composition and volume flow rates of short and long distal tubular fluid can be vastly different.